Question

Imagine we have a force per unit mass of f(x,v) = q(x)p(v).
How would you go about solving for the connection between the
v and the x of an object moving under this force law?  If the
object starts at rest at x=0, what will be its v(x) if the 
the force law is f(x,v) = Ax {nevermind the time}

Answer 1

Given in the question force is the function of x and v

Where x is a distance and v velocity.

Now by using equation v² = u² + 2as where u =0 and as mass is unit given .v² = 2a×1×s

Now a×1 can be considered as force hence replacing from intial eqation.

v² = 2×q(x)×p(v)×x this is the relation between x and v.

Now x=0 and we know force= m×a

And a= (v-u)/t

Replacing as mass is unit and u=0

Ax=v/t

Hence v= Axt

Thanks

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